Explain aditive and multiplicative theoram of probability
Answers
Hi
Here is the answer
Addition Law
Addition LawThe addition law of probability (sometimes referred to as the addition rule or sum rule), states that the probability that AA or BB will occur is the sum of the probabilities that AA will happen and that BB will happen, minus the probability that both AA and BB will happen. The addition rule is summarized by the formula:
will happen and that BB will happen, minus the probability that both AA and BB will happen. The addition rule is summarized by the formula:P(A∪B)=P(A)+P(B)−P(A∩B)
The Multiplication Rule
The Multiplication RuleIn probability theory, the Multiplication Rule states that the probability that AA and BB occur is equal to the probability that AA occurs times the conditional probability that BB occurs, given that we know AA has already occurred. This rule can be written:
P(A∩B)=P(B)⋅P(A|B)P(A∩B)=P(B)⋅P(A|B)
Switching the role of AA and BB, we can also write the rule as:
Switching the role of AA and BB, we can also write the rule as:P(A∩B)=P(A)⋅P(B|A)P(A∩B)=P(A)⋅P(B|A)
Switching the role of AA and BB, we can also write the rule as:P(A∩B)=P(A)⋅P(B|A)P(A∩B)=P(A)⋅P(B|A)We obtain the general multiplication rule by multiplying both sides of the definition of conditional probability by the denominator. That is, in the equation P(A|B)=P(A∩B)P(B)P(A|B)=P(A∩B)P(B), if we multiply both sides by P(B)P(B), we obtain the Multiplication Rule.
Answer:
mark as brain list
Step-by-step explanation:
The multiplication rule states that the probability that A and B both occur is equal to the probability that B occurs times the conditional probability that A occurs given that B occurs.